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Efficient Allocation of a Non-renewable Mineral Resource Over Time

This article delves into the optimal extraction rates and pricing strategies for non-renewable mineral resources, considering factors like market conditions, increasing extraction costs, and the introduction of renewable substitutes. Through graphs and analysis, it explores how marginal extraction costs impact resource utilization over time and the implications for sustainable resource management. The discussion also includes insights on taxation of excess profits, the impact of rents on extraction rates, and the role of savings accounts in influencing resource extraction behavior.

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Efficient Allocation of a Non-renewable Mineral Resource Over Time

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  1. Efficient Allocation of a Non-renewable Mineral Resource Over Time Monday, March 13

  2. Number 1 P = MEC + MUC MUC0 = 4.80 – 2.00 = 2.80 MUC1 = 5.08 – 2.00 = 3.08 Etc. P = 8 – 0.4 q P0 = 8 – 0.4(8.004) = 4.80 P1 = 8 – 0.4(7.305) = 5.08 Etc. 2.80(1.1) = 3.08 3.08(1.1) = 3.39 Etc. MUC increases at the rate of discount (10%)

  3. #1 - Graph P, MEC and MUC over time

  4. Impacts on optimal extraction rates when market conditions change • Number 2 • When a renewable substitute is added • Number 3 • When marginal extraction costs are an increasing function of quantity extracted • Number 4 • Option for efficiency and sustainability

  5. What is the maximum price you would expect for the resource in period 5? Why? Number 2 $6.00 = 8 – 0.4q 0.4q = 2 q = 5 P = 8 – 0.4 q P0 = 8 – 0.4(8.798) = 4.48 P1 = 8 – 0.4(8.177) = 4.73 Etc. If q=5, of depletable is 2.863 units q of renewable is 2.137 units

  6. Number 2 (continued) P = MEC + MUC MUC0 = 4.48 – 2.00 = 2.48 MUC1 = 4.73 – 2.00 = 2.73 … MUC5 = 6 – 2.00 = 4.00 MUC increases at the rate of discount (10%) 2.48(1.1) = 2.73 2.73(1.1) = 3.00 … 3.63(1.1) = 4.00

  7. #2 - Graph P, MEC and MUC over time

  8. Impacts on optimal extraction rates when market conditions change • When a renewable substitute is added: • Opportunity cost of use is lower • The resource is used more quickly

  9. Number 3 P = 8 – 0.4 q P0 = 8 – 0.4(7.132) = 5.15 P1 = 8 – 0.4(6.523) = 5.39 Etc. MEC = 2 + 0.1q MEC0 = 2 + 0.1(7.132) = 2.71 MEC1 = 2 + 0.1(13.66) = 3.37 MEC2 = 2 + 0.1(19.68) = 3.97 Etc. (In this case, q is the cumulative amount extracted.)

  10. Number 3 (continued) P = MEC + MUC MUC0 = 5.15 – 2.71 = 2.44 MUC1 = 5.39 – 3.37 = 2.03 MUC2 = 5.59 – 3.97 = 1.63 MUC is not increasing at the rate of discount. Why?

  11. #3 - Graph P, MEC and MUC over time

  12. What happens to MUC over time if MEC is increasing? $ = MUC MEC + MUC = P MEC TIME

  13. Impacts on optimal extraction rates when market conditions change • When marginal extraction costs are an increasing function of quantity extracted: • The resource is used more slowly since cost is increasing • However, increasing extraction cost means net value declines over time. • Opportunity cost of use declines over time. • Value of foregone resource is less as extraction cost rises

  14. Increases in demand • Increases in population, income, etc. • Expect higher prices for any level of extraction • This means opportunity cost of current extraction is higher • So MUC is higher for every time period than if demand were constant. • What does this mean for the rate of extraction?

  15. Sustainability efforts – building a capital stock (Number 4) • PV of net benefits is $152.17 • In period 0, $35.22 is used • So, period 0 needs to deposit into capital fund enough to insure there is $35.22 at the start of year 8 (first year after mineral is depleted) • x(1.1)8 = 35.22 • 2.144x = 35.22 • X=16.43 – to be paid into fund at time 0 • 16.43(1.1)8 = 35.22 – will be in fund at time 8

  16. PV of net benefits is $152.17 • In period 1, $30.15 is used (in PV terms) • So, period 1 needs to deposit into capital fund enough to insure there is $30.15 at the start of year 8 (first year after mineral is depleted) • x(1.1)7 = 30.15 • 1.949x = 30.15 • X=15.47 – to be paid into fund at time 0 • 15.47(1.1)7 = 30.15 – will be in fund at time 8

  17. Alaska Permanent Fund • www.apfc.org • What is the purpose of the Permanent Fund? • According to language in the state law which established the Permanent Fund (AS 37.13), the Permanent Fund was created with three purposes:(1) to provide a means of conserving a portion of the state's revenue from mineral resources to benefit all generations of Alaskans(2) to maintain safety of principal while maximizing total return(3) to be a savings device managed to allow maximum use of disposable income for purposes designated by law

  18. Policy Question • When Price exceeds MEC, does that mean that the mine owner is earning excess profits and they should be taxed away? • What happens to extraction rate if rents are taxed away?

  19. Your Savings Account $ $ $ $ Use money now Save and use more money later OR

  20. Why would taxing away rents result in faster rate of resource extraction? Q mineral Q mineral Q mineral Q mineral $ mineral $ mineral $ mineral $ mineral Mine and use income now Save, mine later, and use income later OR

  21. Why would taxing away rents result in faster rate of resource extraction? • If mine owner does not get to keep rent, the incentive is to extract the resource quickly and invest the returns in some alternative income-earning venture • e.g. Extract the mineral, sell it, and invest the money at some positive rate of growth

  22. Pt = MECt + MUCt • Can predict changes in price by predicting changes in MEC or MUC • E.G. incident in Middle East • Oil prices rise • Price gouging? Or increase in MUC? • Once more certainty in availability is established, MUC goes back down

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